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Proof step 29 from proof read-loop-inv (previous step)

VFS_PAGE_SIZE = n4 + (n0 + n3) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, m4, content), n0 + n3 < m2, n0 + n3 < n1, read-inv(n0, n1, mkinode(m, md, boolvar, m0, m1, m2), buf2, buf1, n3, dirs, files), read-inv(n0, n1, mkinode(m, md, boolvar, m0, m1, m2), buf2, buf3, n2, dirs, files), (n0 + n3) % VFS_PAGE_SIZE + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ # getpage((n0 + n3) / VFS_PAGE_SIZE, content), n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ # buf1 ⊦ m2 = n0 + n3, n1 = n0 + n3, n4 = 0, afs-cons(dirs, files) ∧ # buf2 = # buf1 ∧ m ∈ files ∧ m3 = m2 ∧ n0 + n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ n1 ∧ n0 + n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ m2 ∧ n1 ≤ # buf2 + n0 ∧ read-inv (n0, n1, buf2, copy(getpage((n0 + n3) / VFS_PAGE_SIZE, content), (n0 + n3) % VFS_PAGE_SIZE, buf1, n3, min(n1 - n0 + n3, n4, m2 - n0 + n3)), n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3), content)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ read-inv(n0, n1, inode, buf0, buf1, n, dirs, files) ↔ afs-cons(dirs, files) ∧ # buf0 = # buf1 ∧ inode.ino ∈ files ∧ files[inode.ino].size = inode.size ∧ n0 + n ≤ n1 ∧ n0 + n ≤ inode.size ∧ n1 - n0 ≤ # buf0 ∧ read-inv(n0, n1, buf0, buf1, n, files[inode.ino].content)
Proof step 31:
# buf2 = # buf1, files[mkinode(m, md, boolvar, m0, m1, m2).ino].size = mkinode(m, md, boolvar, m0, m1, m2).size, VFS_PAGE_SIZE = n4 + (n0 + n3) % VFS_PAGE_SIZE, files[m] = mkfile(m3, md0, m4, content), n0 + n3 < n1, n0 + n3 < m2, afs-cons(dirs, files), read-inv(n0, n1, mkinode(m, md, boolvar, m0, m1, m2), buf2, buf3, n2, dirs, files), read-inv(n0, n1, buf2, buf1, n3, files[mkinode(m, md, boolvar, m0, m1, m2).ino].content), mkinode(m, md, boolvar, m0, m1, m2).ino ∈ files, n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ # buf1, (n0 + n3) % VFS_PAGE_SIZE + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ # getpage((n0 + n3) / VFS_PAGE_SIZE, content), n0 + n3 ≤ n1, n0 + n3 ≤ mkinode(m, md, boolvar, m0, m1, m2).size, n1 - n0 ≤ # buf2 ⊦ m2 = n0 + n3, n1 = n0 + n3, n4 = 0, afs-cons(dirs, files) ∧ # buf2 = # buf1 ∧ m ∈ files ∧ m3 = m2 ∧ n0 + n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ n1 ∧ n0 + n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3) ≤ m2 ∧ n1 ≤ # buf2 + n0 ∧ read-inv (n0, n1, buf2, copy(getpage((n0 + n3) / VFS_PAGE_SIZE, content), (n0 + n3) % VFS_PAGE_SIZE, buf1, n3, min(n1 - n0 + n3, n4, m2 - n0 + n3)), n3 + min(n1 - n0 + n3, n4, m2 - n0 + n3), content)

Rule argument

spec: <toplevel> name: read-inv-strong seq: ⊦ read-inv(n0, n1, inode, buf0, buf1, n, dirs, files) ↔ afs-cons(dirs, files) ∧ # buf0 = # buf1 ∧ inode.ino ∈ files ∧ files[inode.ino].size = inode.size ∧ n0 + n ≤ n1 ∧ n0 + n ≤ inode.size ∧ n1 - n0 ≤ # buf0 ∧ read-inv(n0, n1, buf0, buf1, n, files[inode.ino].content) subst: [files, dirs, n, buf1, buf0, inode, n1, n0] → [files, dirs, n3, buf1, buf2, mkinode(m, md, boolvar, m0, m1, m2), n1, n0] flags: <all paths>

Additional information

Used terms: files, dirs, n3, buf1, buf2, mkinode(m, md, boolvar, m0, m1, m2), n1, n0